Abstract

July 2 - 10.50-11.40
F. Komaki - Information Geometry of Statistical Prediction

Bayesian predictive distributions are investigated from the viewpoint of information geometry. Kullback-Leibler divergence from the true distribution to a predictive distribution is adopted as a loss function. We show that there are many examples where the Bayesian predictive distribution based on the Jeffreys prior is dominated by Bayesian predictive distributions based on other priors. It is shown that the Bayesian predictive distribution based on the right invariant measure is the best invariant predictive distribution when a model has a group structure. Furthermore, we show that there exist shrinkage predictive distributions asymptotically dominating Bayesian predictive distributions based on the Jeffreys prior or other vague priors if the model manifold satisfies some differential geometric conditions. We show several examples where shrinkage predictive distributions exactly dominate Bayesian predictive distributions based on vague priors. [an error occurred while processing this directive]